Mutual Consensus and its Application in Minimum Cost Consensus Models

TL;DR

This paper proposes a new mutual consensus measure for robust group decision-making, introduces novel MCC models, and demonstrates their effectiveness in preference aggregation and approximate solutions.

Contribution

It introduces the concept of mutual consensus, develops new MCC models based on it, and applies these models to OWA-based preference aggregation for improved decision-making.

Findings

Mutual consensus effectively captures maximum opinion disparity.

New MCC models are formulated and analyzed for properties.

Mutual consensus enhances approximate solutions in OWA-MCC models.

Abstract

This paper introduces the concept of {mutual consensus} as a novel non-compensatory consensus measure that accounts for the maximum disparity among opinions to ensure robust consensus evaluation. Incorporating this concept, several new Minimum Cost Consensus (MCC) models are proposed, and their properties are analyzed. To show their applicability, these mutual consensus-based MCC models are then considered in the context of the {OWA-MCC} model, which employs Ordered Weighted Averaging (OWA) operators for preference aggregation. Concretely, we include a linearized formulation under symmetry conditions as well as examples of the non-convexity of the feasible region in the general case. Finally, mutual consensus is utilized to obtain approximate solutions for the OWA-MCC model, demonstrating its practical effectiveness and advancing the theoretical and applied dimensions of consensus modeling in group decision-making.